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Before banning, Modern also had "Hypergenesis," using cascade tricks to set up a super-fast Hypergenesis.

Legacy "Elves" is an occasionally-successful but easy-to-hate deck that chains a ton of mana dorks, usually with Glimpse of Nature, to hardcast Emrakul.

Vintage has "Oath," which uses Oath of Druids (banned in Legacy) to cheat out Eldrazi.

You can take inspiration from a variety of other decks that access huge amounts of mana, such as "High Tide," "Amulet of Vigor," "Enchantress" (via Serra's Sanctum, mainly), and "MUD" (via Metalworker and Cloudpost). Many of these don't actually need a card like Emrakul to win but sometimes play it anyway because it goes "over the top" of many other strategies.

Other approaches I've seen used (ranked in approximate order of jankiness):

Polymorph and a bunch of token-generating cards like Lingering Souls (which make creatures on the battlefield but aren't creature cards themselves).

Instant-speed reanimation with Goryo's Vengeance or Shallow Grave. The classic reanimator spells like Exhume or Unburial Rites don't work because the big three shuffle themselves back into your library, but you can still use Goryo's Vengeance in response to the trigger.

Sneak and Show for Legacy: it was totally the top deck for a while. Main down side is that it was totally the top deck for a while, of course, so many players know how to play against it.

G/R Tron for Modern. Faster and more consistent than the other Tron decks, and pretty cheap to put together, especially if you already own the Eldrazi. The main down side is that it is pretty weak against some of the other combo decks (like Storm) and hyper-aggressive decks.

If you're looking for a deck to play at "casual" tables, my recommendation is a Windbrisk Heights + Summoning Trap deck. It's still very powerful but not as obviously "unfair" as the tournament combo decks — some players vehemently dislike seeing turn-3 Karn every other game — and the aggressive/midrange creatures give you a decent fallback plan even if the whole table is dedicated to hating out your combo.

+1 Nice extensive answer. For casual, don't forget [mtg:Mana Echoes] the token generating drones, and the Eldrazi that gets copies you own from outside the game
– user1873Jul 6 '12 at 16:26

I'm just a casual player I just checked out the Eldrazi cards and I wanted to put together a nice deck.
– Adam AroldJul 6 '12 at 19:48

2

Only other major competitive deck I think you missed is Doomsday + Shelldock Isle, although that deck is possibly one of the hardest to play in existence.
– WLPhoenixJul 24 '12 at 22:06

a little nit picky - but I don't believe there was ever a point where hypergenesis wasn't banned. I think it was on the banlist for the community cup which was the first test of modern, and has been ever since
– PattersOct 24 '14 at 8:37

@Faults, Because although they are colorless, the legendary Eldrazi are not artifacts, and thus not legal choices for Tinker. (Tinker is also banned in all official formats except Vintage and MTGO's "Classic" -- and it's restricted to 1/deck in both of those!)
– Brian SDec 10 '13 at 22:57

3) The harder way: Urza lands like Urza Incubator, as well as the Urza land combo.

4) 12 post the crap out of it!

All of these ways are how my deck works, and I have been able to Emrakul, the Aeons Torn on turn 4 multiple times; as well as being able to play Eldrazi left and right by turn 6 and quickly take control of the game.

Welcome to the site! I have made some grammatical and formatting updates to your post; please note that as a Q&A site, as opposed to a standard forum; such things are more important. Your answers will be much better received, and you will receive more reputation, if you take a little care with your posts.
– GendoIkariOct 4 '14 at 5:24

He literally never came back after that day. Guess it was too much to handle.
– temporary_user_nameOct 26 '15 at 20:16

Decks like Eldrazi Spawn rely on swarming the field with Eldrazi Spawn tokens that you can sacrifice for colorless mana. If you manage to get Growth Spasm in play, it becomes really easy to spam the field with tokens and play the big three.